Multirate zero-forcing Tx-Rx design for MIMO channel under BER constraints

This paper is concerned with communicating parallel independent streams of data, possibly of different rates, through a multiple-input multiple-output channel. Each data stream is required to satisfy a bit-error-rate (BER) constraint. This scenario arises in multimedia communications. We find the linear zero-forcing transmitter-receiver (Tx-Rx) matrix pair that requires the minimum transmitter power to achieve the BER constraints. It is well known that the Tx-Rx pair can be chosen to partition the matrix channel into scalar subchannels corresponding to singular values, and different data streams can be transmitted through different subchannels. This design is suboptimum in general. The optimum design has the following structure. The set of input data streams is partitioned into groups called signal groups. The set of subchannels is conformably partitioned into subchannel groups. Each signal group is collectively transmitted through its assigned subchannel group. With each signal/subchannel group pair is associated a unitary matrix that mixes the signals at the transmitter and unmixes them at the receiver. We derive a simple algorithm to determine the optimum signal and subchannel groups. We then use a known algorithm from majorization theory to determine the unitary matrices. Using these, we completely specify the optimum Tx-Rx pair.